You need a SOLID shooting bench (doesn't move at all).
You need sandbags. You can make your own but Walmart sells a nice set of shooting rests at a good price.
You need to correct for parallax at your desired range (you said 50 yards, right?). This means either an adjustable objective scope, or adjust your non-AO scope to be free of parallax at 50 yards.
Now you're ready to shoot. Get several different kinds of ammo because each rifle has its likes and dislikes. I tell people to start with the CHEAPEST ammo you can find and then work your way up the price scale until you find something that is producing what YOU consider to be good accuracy for the price. (For some people, "only the best will do," regardless of price. I'm not that picky.)
If your 10/22 is typical, it should produce 50 yard groups of 1.5 to 2 inches. If groups are much over 2 inches with several types of ammo, something is wrong, either with your rifle or with your shooting technique. If you are lucky, you might find a brand of inexpensive ammo that will group 1.25 to 1 inch even at 50. If you are REALLY lucky, you might even find an ammo that will shoot into under an inch, but don't count on this or be disappointed if you don't. If you can get into the 1 to 1.25 inch group range with a stock 10/22, you're doing pretty well.
I have no experience with Charger or 96/22 so cannot comment on those.